Phenomenology of the Neutrino-Mass-Giving Higgs Triplet and the Low-Energy Seesaw Violation of Lepton Number

Abstract

Small realistic Majorana neutrino masses can be generated via a Higgs triplet $({\xi }^{++},{\xi }^{+},{\xi }^0)$ without having energy scales larger than $M_{\ast }=\mathcal{O}(1)$ TeV in the theory. The large effective mass scale $\Lambda$ in the well-known seesaw neutrino-mass operator ${\Lambda }^{-1}(LL\Phi \Phi )$ is naturally obtained with $\Lambda \sim M_{\ast }^2/\mu ,$ where $\mu$ is a {\it small} scale of lepton-number violation. In theories with large extra dimensions, the smallness of $\mu$ is naturally obtained by the mechanism of ``shining'' if the number of extra dimensions $n\ge 3.$ We study here the Higgs phenomenology of this model, where the spontaneous violation of lepton number is treated as an external source from extra dimensions. The observable decays ${\xi }^{++}\to l_i^{+}{l}_j^{+}$ will determine directly the magnitudes of the $\{ij\}$ elements of the neutrino mass matrix. The decays ${\xi }^{+}\to W^{+}{J}^0$ and ${\xi }^0\to Z{J}^0$, where $J^0$ is the massless Goldstone boson (Majoron), are also possible, but of special importance is the decay ${\xi }^0\to J^0{J}^0$ which provides stringent constraints on the allowed parameter space of this model. Based on the current neutrino data, we also predict observable rates of $\mu -e$ conversion in nuclei.

Comments: Minor changes in the text, results unchanged